[tex] \sqrt[3]{4} \times \sqrt[3]{16} - \frac{ \sqrt[4]{512} }{ \sqrt[4]{2} } = \sqrt[3]{4 \times 16} - \sqrt[4]{ \frac{512}{2} } = \\= \sqrt[3]{4 \times {4}^{2} } - \sqrt[4]{256} = \sqrt[3]{4 {}^{3} } - \sqrt[4]{ {4}^{4} } = 4 - 4 = 0[/tex]